Rare Events and Poisson Point Processes

Abstract

The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent terms by the accompanying compound Poisson laws may be interpreted as rather sharp quantitative estimates for the closeness between the sample containing independent observations of rare events and the Poisson point process which is obtained after a Poissonization of the initial sample.

Convergence to infinite-dimensional compound Poisson distributions on convex polyhedra

“…The situation considered in Theorem 2 can be interpreted as a comparison of a sample containing independent observations of rare events (like disasters, epidemics, accidents, bankruptcies etc.) with the Poisson point process which is obtained after a Poissonization of the initial sample (see [3], [14]). Let Y 1 , Y 2 , .…”

Estimates for the closeness of convolutions of probability distributions on convex polyhedra

“…The situation considered in Theorem 2 can be interpreted as a comparison of the sample containing independent observations of rare events with a Poisson point process which is obtained after a Poissonization of the initial sample (see [3], [14]).…”